Earnest called the Texas senator’s comments another unprecedented step in the contentious fight to replace the late Justice Antonin Scalia.

Senate GOP leaders have already pledged not to hold hearings or votes for any nominee Obama puts forward, arguing it should be up to the next president, and not Obama, to name a replacement for the conservative judge.

Now, they have “taken the next step and suggested without knowing who this nominee is … that they’ll be subjected to bashing by Republicans,” Earnest said.

He said it’s "an indication that Republicans are digging in even further on an unreasonable position of not giving that person any sort of fair hearing and vowing to tear that person down."

He added: "I don’t think that’s how most people believe how this process should work."

Cornyn responded that he wouldn't "be preached to" by Reid or other Democrats, noting their 2013 decision to invoke the "nuclear" option that allowed many lower court judicial nominees to be confirmed by a simple majority vote in the Senate.

"I would be surprised if any person who actually aspired to be on the United States Supreme Court ... would allow themselves to be used by this administration," he added.